Best Known (72−44, 72, s)-Nets in Base 27
(72−44, 72, 114)-Net over F27 — Constructive and digital
Digital (28, 72, 114)-net over F27, using
- t-expansion [i] based on digital (23, 72, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(72−44, 72, 172)-Net in Base 27 — Constructive
(28, 72, 172)-net in base 27, using
- 12 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 63, 172)-net over F81, using
(72−44, 72, 208)-Net over F27 — Digital
Digital (28, 72, 208)-net over F27, using
- t-expansion [i] based on digital (24, 72, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(72−44, 72, 244)-Net in Base 27
(28, 72, 244)-net in base 27, using
- 4 times m-reduction [i] based on (28, 76, 244)-net in base 27, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
(72−44, 72, 16828)-Net in Base 27 — Upper bound on s
There is no (28, 72, 16829)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 11 438481 824378 800144 707794 502583 538798 773264 897507 986534 234879 455267 363094 616959 345359 884097 725193 012769 > 2772 [i]